( ) : 1997

( ) 2008 2 17 : 1997

CMOS FET AD-DA All Rights Reserved (c) Yoichi OKABE 2000-present. [ HTML ] [ PDF ] [ ] [ Web ] [ ] [ HTML ] [ PDF ] 1

1 4 1.1..................................... 4 1.2.................................. 5 1.3......................................... 7 2 9 2.1 n-mos FET................................. 9 2.2.................................... 11 2.3 p-mos FET................................. 13 2.4................................. 13 3 15 3.1.................................. 15 3.2..................................... 17 3.3.................................. 18 3.4................................. 19 3.5 p-mos...................................... 19 3.6 c-mos...................................... 20 3.7 SEP....................................... 20 3.8.................................. 20 4 21 4.1......................................... 21 4.2 (NOT )................................ 21 4.3 NAND NOR............................... 24 4.4 c-mos......................... 25 4.5.................................. 27 4.6.................................. 30 4.7......................................... 31 4.8......................................... 31 4.9........................................... 31 4.10...................................... 31 5 33 5.1............................... 33 5.2......................................... 33 5.3................................ 34 2

5.4................................. 36 5.5.......................................... 37 5.6......................................... 37 5.7....................................... 37 5.8.......................................... 38 5.9.................................... 39 5.10.................................... 40 6 41 6.1..................................... 41 6.2 LPF................................... 41 6.3................................ 42 6.4................................. 43 6.5 HPF BPF BSF............................. 44 6.6.................................. 45 6.7 AD.................... 46 6.7.1................................... 46 6.7.2............................... 48 6.7.3 AD................ 50 3

1 1.1 (electronic circuit) (device) 1.1 FET FET 1.1: 4

FET FET 1.2 10 C 11 C 1K 10.1 C 10.11 C (analog) (digital) 0 1 1.2 5

1.2: 1.3: 0 1 0 1 1960 ( ) 1mm 1µm A/D D/A 1.3 PCM ( ) 6

1.3 IC (integrated circuit) FET IC (monolithic IC) ( ) IC IC FET IC IC (hybrid IC) NOT AND OR IC 1.4 SSI (small scale integration) MSI (medium...) LSI (large...) VLSI (very large...) ULSI (ultra large...) ELSI (extra large...) cm 2 7

1.4: 8

2 2.1 n-mos FET FET FET (field effect transistor) (bipolar transistor) - 2.1: n-mos FET FET 2.1 FET (drain) (source) (gate) FET (negative) FET n-mos FET MOS FET (metal) (oxide) (semiconductor) FET (positive) p-mos FET p-mos FET n-mos FET C g Q = C g V gc = εlw V gc (2.1) t L W t V gc 9

Q f Q + Q f = εlw t Q f Q = εlw t V th V gc (2.2) (V gc V th ) (2.3) V ds v = µe (2.4) µ L E = V ds L (2.5) t = L v (2.6) Q I d = Q t = C g(v gc V th ) v L = µεw Lt (V gc V th )V ds (2.7) V gc V gc = (V gs + V gd )/2 = V gs V ds /2 I d = µεw Lt ( V gs V th V ) ds V ds (2.8) 2 V gs V th 0 V gd V th 0 I d V ds 2.2 V ds V gs V th ) - - V gs V ds I d V gs I d V ds I d -V ds I d -V ds - I d V ds 10

2.2: n-mos n-mos FET n-mos FET V ds V ds 0 V gs V th x V gd V th A = µεw Lt ( I d = A V gs V th V ) ds V ds : 0 V gs V th V ds 2 I d = 0 : 0 V gs V th (2.9) I d = A 2 (V gs V th ) 2 : V ds V gs V th (2.10) 2.2 11

2.10 d s I d I d V gd = V gs V ds V sd = V ds ( I d = A V gs V th V ) ds V ds : V ds V gs V th 0 (2.11) 2 I d = 0 : V ds V gs V th (2.12) I d = A 2 (V gs V th V ds ) 2 : 0 V gs V th (2.13) 2.3 2.3: n-mos 2.1 I d I d ( I d = A V gd V th V ) sd V : sd 0 V gd V th V sd (2.14) 2 I d = 0 : 0 V gd V th (2.15) I d = A 2 (V gd V th ) 2 : V sd V gd V th (2.16) 12

2.3 p-mos FET FET p-mos FET V ds /le0 I d I d < 0 A = µεw Lt (2.17) ( I d = A V gs V th V ) ds V : ds 0 V gs V th V ds (2.18) 2 I d = 0 : 0 V gs V th (2.19) I d = A 2 (V gs V th ) 2 : V ds V gs V th (2.20) V ds V ds > 0 ( I d = A V gs V th V ) ds V : ds V ds V gs V th 0 (2.21) 2 I d = 0 : V ds V gs V th (2.22) I d = A 2 (V gs V th V ds ) 2 : 0 V gs V th (2.23) 2.4 2.4 2.4: p-mos 2.4 FET npn pnp 2.5 npn (emitter) (collector) (base) 13

2.5: npn 2.6: V be V ce I c V ge 2.6 FET 1/100 14

3 3.1 NOT AND OR 0 1 0 1 - V gs I d I d 3.1 n-mos FET FET ( ) FET V dd V dd FET 3.2 V gs I d V ds FET V ds FET V dd RI d I d V ds FET V ds I d V ds 3.3 V gs V gs V ds I d 3.4 3.5 3.1: n-mos FET 15

3.2: Vgs 3.3: V gs 3.4: - 3.5: 16

3.6: V th 0 3.2 3.6 V dd FET 10 V gs V ds FET I d FET 17

3.7: 3.8: 3.3 3.7 FET FET - V gs V gs V gs FET FET I d V gs V gs V gs FET FET FET FET FET FET V gs 3.8 1 FET - 18

3.9: n-mos FET 1 1 3.4 3.9 = = 0 1 0 1 1 0 0 1 NOT ( Inverter) 1 0-1 1-1 n-mos 1 0 1 3.5 p-mos p-mos FET p-mos FET + + 3.10 + FET FET n-mos FET p-mos FET R 19

3.10: p-mos FET 3.11: p-mos FET FET R FET 3.11 3.6 c-mos 3.7 SEP 3.8 20

4 4.1 0 1 0 1 0 1 ( ) (sequential logic circuit) 4.1 0 1 0 1 (combinational logic circuit) 4.2 (NOT ) FET 1 FET (NOT ) 4.2 n-mos 4.3 n-mos FET MOS - - (metal-oxide-semiconductor) FET - n-mos n (negative) n-mos 1 0 4.1: 21

4.2: n-mos (NOT ) 4.3: n-mos FET 4.4: p-mos FET 4.5: p-mos (NOT ) 22

4.6: c-mos (NOT ) 4.7: c-mos 4.4 FET p-mos FET p-mos FET p-mos FET p-mos 4.5 p-mos n-mos 0 1 FET 1 c-mos c- MOS c-mos 4.6 n-mos p-mos n-mos p-mos p-mos n-mos p-mos FET MOS c-mos (complimentary MOS) n-mos FET p-mos FET 4.7 V o FET n-mos FET n-mos FET V ds n-mos FET p-mos FET p-mos FET V ds V dd V o p-mos FET V dd I d FET FET 4.8 n-mos FET Vth n (a) n-mos FET (V dd 0) V dd (b) V dd /2 (c) (c) 23

4.8: c-mos 4.9: c-mos (d) V dd V dd V p th p-mos FET (0, 0) 4.9 FET 4.10 4.9 n-mos p-mos V dd 0 V dd 0 V dd 0 c-mo S 4.3 NAND NOR NOT AND OR AND 1 1 OR 1 1 ON ON ON FET AND OR NAND NOR 4.10: c-mos 24

4.11: c-mos NAND 4.12: c-mos NOR c-mos NAND NOT 1 FET ON FET OFF NAND 1 ON OFF 4.11 n-mos FET p-mos FET 0 n-mos OFF p-mos ON 1 NOR 4.12 Buffer AND OR AND NAND OR NOR XOR 4.4 c-mos c-mos 0 (intrinsic delay) n- p-mos FET R c C g τ 0 = C g R c - FET τ 0 τ 0 = C g R c = L v = τ t (channel transit time) L2 µv ds = τ t (4.1) 25

(extrinsic delay) 0V V dd p-mos p-mos ( ) R c τ = CR c n-mos n-mos p-mos p-mos R c (n-mos p-mos ) C = fc g (4.2) τ = fτ 0 (4.3) n- p-mos FET C CVdd 2 /2 p-mos n-mos 0 CVdd 2 /2 V dd CV dd CVdd 2 CV dd 2 /2 CVdd 2 /2 p-mos f c P 0 = f c CV 2 dd/2 (4.4) C = fc g p P = pfp 0 (4.5) NAND NOR NAND NOR (fan in) n-mos p-mos 26

FET NAND NOR NAND NOR AND NOR NAND NAND ( fan out) FET f t n f f n = f t (4.6) fτ 0 τ t τ t = nfτ 0 (4.7) log n τ t = f τ 0 log f log f t (4.8) f f = e e log f t 2 3 f = 10 f = e 1.6 4.5 AND OR NOT (truth table) 4.13 D (000) 1 (000) (0 0 0) S 0 S 0 = A B C (4.9) 27

4.13: NOT AND A A AND AND (A B C) (000) (A, B, C) (111) AND (111) 1 (A B C) (000) 1 2.13 S 0 S 7 S 0 = A B C (4.10) S 1 = A B C (4.11) S 2 = A B C (4.12) S 3 = A B C (4.13) S 4 = A B C (4.14) S 5 = A B C (4.15) S 6 = A B C (4.16) S 7 = A B C (4.17) D (001), (010), (100), (111) 1 1 OR D = S 1 + S 2 + S 4 + S 7 = A B C + A B C + A B C + A B C (4.18) NOT AND OR OR + AND + AND AND OR E = S 3 + S 5 + S 6 + S 7 = A B C + A B C + A B C + A B C (4.19) 0 1 NOT AND OR AND OR NAND NOR S 0 S 7 28

4.14: NAND-NAND 4.15: NAND-NAND T 0 T 7 T 0 = A B C (4.20) T 1 = A B C (4.21) T 2 = A B C (4.22) T 3 = A B C (4.23) T 4 = A B C (4.24) T 5 = A B C (4.25) T 6 = A B C (4.26) T 7 = A B C (4.27) D = T 1 + T 2 + T 4 + T 7 D = T 1 T 2 T 4 T 7 NOT NAND OR(NOT) NAND De Morgan D 0 OR OR 1 1 OR 0 0 T 1 T 7 T 1 T 7 T 1 T 7 1 D 0 1 AND 1 NAND 0 T 1 T 7 1 0 4.14 4.15 NAND 4.13 NAND 1 A B C 29

4.16: D Flip Flop 0 A B C NAND 1 NAND NAND-NAND NAND NOR S 0 = A + B + C S 1 = A + B + C S 2 = A + B + C S 3 = A + B + C S 4 = A + B + C S 5 = A + B + C S 6 = A + B + C S 7 = A + B + C (4.28) de Morgan S 0 OR (000) 0 NOR 1 D S 0 S 3 S 5 S 6 0 D = S 0 + S 3 + S 5 + S 6 (4.29) NOR-NOR 0 NOR-NOR NAND-NAND (inversion logic) 4.6 ( ) 4.16 FET FET t 0 t 1 A B B t 1 B A t 1 t 2 B C 30

D t 2 C B D A B D A t 0 t 1 B 4.7 1 1 4.8 4.9 4.10 IC MOS-IC IC MOS-IC [1.4] FET C-MOS 35 IC ( 13) IC 1cm 2 31

1 IC IC 35 IC IC IC IC IC 32

5 5.1 FET IC Operational Amplifier FET 5.2 5.1 V in R 1 R 2 I = V i /(R 1 + R 2 ) V o = R 1 I = V i R 1 /(R 1 + R 2 ) 5.2 R 1 R 1 + R 2 R 3 R 3 + R 4 5.1: 33

5.2: + 5.3: 5.3 10MΩ 1Ω 100,000 5.3 ± 15V 5.4 34

+ 5.4: V V + A V o V o = A(V + V ) = AV (5.1) V V o V V = R f V i + R i V o R i + R f (5.2) V V i V o V 1/A A, R f /R i V o = 1 + (1 + R f /R i )/A V i (5.3) V o = R f R i V i (5.4) A (inverter) A 5.2 A V o V = V + (5.5) (imaginary short) V + V 0V 5.2 R i V i /R i R f R f V i /R i V o = R f V i /R i R f /R i 35

5.5: 5.5 V i V o V R i : R f 0 ±15V V i V o 15V 15V V o 15V V V i +15V A A 10 5 10 4 G i /G f 100 5.3 100/1.01 = 99 1% A A 1% 10 4 A A 1% 2% A 2 10 6 A 10 6 1% R i R f? (1Ω ) (10MΩ ) 100Ω 100kΩ 5.4 5.4 V o 36

5.5 5.6 Q V Q = CV I I = C, dv/dt V = V 0 sin ωt I = ωcv cos ωt I 0 V 0 I 0 /V 0 = ωc ω I 0 V 0 22 I 0 V 0 Φ I Φ = LI V V = L, di/dt V 0 /I 0 = ωl HPF, high pass filter 23???? 24 (LPF, low pass filter ) (BPF band pass filter ) 5.7 2 2 FET V I V = A 0 + A 1 I + A 2 I 2 + A 3 I 3 + 37

I 2 I 3 I 2 I I = I 0 cos ωt I o cos ωt I 0 sin ωt I = I1 2 cos 2 ωt = 1 2 (I2 1 + I1 2 cos 2ωt) 1 2 2 I I = I 1 cos ω 1 t + I 1 cos(ω 1 2 + θ) I 2 = 1 2 I2 1 + 1 2 I2 2 )+ 1 2 I2 1 cos 2ω 1 t+ 1 2 I2 2 cos 2ω 2 t+i 1 I 2 cos[(ω 1 ω 2 )t+θ)]+i 1 I 2 cos[(ω 1 +ω 2 )t+θ)] 3 4 ω 1 ω 2 5 6 2 nω 1 + mω 2 n m 26?? V in V in V out V in V in V in V out V out = 0 V out?? V in 27???? V in V out V in V out V out 5.8? 28 29?? B A A V in B V out 29?????? f 0 (V out /V in ) 38

f = f 0 1 28 B A A f 0 1 B A f 0 29?? V 0 f 0 V 0 FET 3 5.9 FET 18?? I b I c I in = 0 I b I c 8?? 0.6V 4V 34kΩ (4-0.6)V/34kΩ =0.1mA I b ( ) Ic I b = 0.1mA I c V ce I b = 0.1mA 100Ω 100I c V V ce = 4 100I c V?? I b = 0.1mA I c = 10mA V ce = 3V 0.1mA I in I c I in = 0.1mA I b = 0.2mA I c 10mA 20mA I in 0.1mA I c 100 10mA β 100Ω 19 I b V be V in 0.6V I in I in β I c 100Ω (V out /V in ) 0.6V V in 3V V out 39

FET FET V gs V in ( ) V dd R ( ) V in V ds V th FET 20 5.10 3.4 40

6 6.1 (low pass filter, LPF) (high pass filter, HPF) (band pass filter, BPF) (band rejection filter, BRF) 6.2 LPF LPF ω = 1 LPF LPF LPF RC R C C C C x y y = 1 1 + CRs x (6.1) ω s = jω (c.c. ) y ( 2 1 = x 1 + jcrω ) c.c. = 1 1 + (CRω) 2 (6.2) y 1 = x 1 + (CRω) 2 (6.3) ω = 0 100% ω ω = 1/CR 1/ 2 0 LPF s ω y = 1 s n x (6.4) 41

s y 1 = x ω 2 n (6.5) ω 2 s s = jω ±ω s 6.3 (Butterworth) x n n x = 1 1 n ω < 1 100% ω > 1 0% x = 1 y 1 = x 1 + ω 2n (6.6) s n = 2 n y 2 1 = x 1 + ω 4 (6.7) jω jω 0 jω α i (jω α i ) y 2 1 = x 1 + ω 4 = 1 (jω + (1 + j)/ 2)(jω + (1 j)/ 2)(jω (1 + j)/ 2)(jω (1 j)/ 2) ( ) 1 = (jω + (1 + j)/ 2)(jω + (1 j)/ (c.c.) (6.8) 2) jω s s y = 1 (s + (1 + j)/ 2)(s + (1 j)/ 2) x = 1 s 2 + 2s + 1 x (6.9) (jω α i ) 4 α i L C R 42

6.7 ω s/j s s s = 0 1 s k = sin (2k 1)π 2n + j cos (2k 1)π 2n k = 1, 2,, 2n (6.10) 1 2n 6.4 (Chebyshev) cos(n cos 1 ω) ω 1 C n (ω) = cosh(n cosh 1 ω) ω > 1 (6.11) ω <= 1 1 n (Lissajou) ω = 1 1 ω = 1 ±1 pm1 n 1 n ω > 1 ± ω C 1 (ω) = ω (6.12) C 2 (ω) = 2ω 2 1 (6.13) C 3 (ω) = 4ω 3 3ω (6.14). (6.15) C n (ω) = 2ωC n 1 (ω) C n 2 (ω) (6.16) y 1 = (6.17) x 1 + ɛ2 C n (ω) 2 ω 1 C n (ω) 2 0 1 100% 1/ 1 + ɛ 2 ɛ ω > 1 1/ω n 43

s s k = sinh ( ) ( ) 1 1 (2k 1)π 1 1 (2k 1)π n sinh 1 sin + j cosh ɛ 2n n sinh 1 cos ɛ 2n (6.18) 6.10 n ɛ 6.5 HPF BPF BSF ω = 1 LPF ω c LPF s s s/ω c LPF K a 0 b 1 s + a 0 s 2 + 2a 1 s + b 2 1 b n s 2 + 2a n s + b 2 n (6.19) K 1 1 a < b s = 0 1 s 0 ω c HPF ( ) s ω c /s HPF K s s 2 s + a 0 s 2 + 2a 1 s + b 2 1 s 2 + 2a n s + b 2 n s 2 (6.20) BPF ( ) ω l ω u LPF ω = 1 ω = 1 BPF -1 ω l 1 ω u ω = Aω B ω (6.21) ω LPF 1 = Aω l B ω l 1 = Aω u B ω u (6.22) (6.23) A B 1 A = ω u ω l (6.24) B = ω uω l ω u ω l (6.25) 44

A B ω s/j s LPF s As + B/s BPF 2a 1 s 2a n s K s 2 + 2a 1 s + b 2 1 s 2 + 2a n s + b 2 n (6.26) BSF ( ) s s 1/(As + B/s) BSF s 2 + b 2 1 s 2 ( ) + b n 2a 1 s 2a n s K s 2 + 2a 1 s + b 2 1 s 2 + 2a n s + b 2 = K 1 n s 2 + 2a 1 s + b 2 1 s 2 + 2a n s + b 2 n (6.27) 6.6 L C R L C R s Y f Y f V i Y i V Y i - + Y g V o 6.1: 6.1 (MFB: multiple feedback type active filter) 0 Y i V i + Y f V o = (Y i + Y f + Y g + Y i )V (6.28) Y i V + Y f V o = 0 (6.29) Y i Y i (Y i + Y f + Y g + Y i )Y f + Y i Y f (6.30) Y i Y g = 0 Y i Y f + Y f (6.31) 45

K a s + a : Y i, Y g = 0, Y f = Cs, Y f = G = ac, Y i = KG (6.32) K s s + a : Y i, Y g = 0, Y f = Cs, Y f = G = ac, Y i = KCs (6.33) b 2 s 2 + 2as + b 2 : Y f = Cs, Y f = G = b2 a C, Y i = KG, Y i = (K + 1)G, ( ) 2 b Y g = (K + 1) Cs (6.34) a Ks 2 s 2 + 2as + b 2 : Y i = Y i = Cs, Y f = 1 K Cs, Y a f = K + 1/2 C, Y g = b2 (K + 1/2) C (6.35) ak LPF HPF BPF BSF BPF BSF = 1 BP F V i BPF V i 6.7 AD (oversampling method) AD (AD convertor) 12 bit ( ) 1 bit AD (AD conversion) bit AD (over-sampling) 1 bit AD Σ AD 6.7.1 x + - y Integrator S/H 6.2: AD (delta modulation) 6.2 D (Sample/Hold) 46

± 6.3 + / 1/ 1 1-1 15 input output sum 10 5 0-5 -10 0 20 40 60 80 100 120 6.3: 6.4 47

1400 power 1200 1000 800 600 400 200 0-60 -40-20 0 20 40 60 6.4: 0 6.7.2 x + - Integrator y S/H 6.5: 6.3 6.5 6.6 48

25 input output sum 20 15 10 5 0-5 0 20 40 60 80 100 120 6.6: 6.7 1400 power 1200 1000 800 600 400 200 0-60 -40-20 0 20 40 60 6.7: 49

6.7.3 AD AD (sigma-delta AD convertor) AD AD AD AD AD bit (oversampling method) 12 bit 2 12 s 50

band stop filter, BSF, 41, 41 AD conversion (AD ), 46 AD convertor (AD ), 46 AD (AD conversion), 46 AD (AD convertor), 46 band pass filter, BPF ( ), 41 band rejection filter, BRF ( ), 41 delta modulation ( ), 46 high pass filter, HPF ( ), 41 low pass filter, LPF ( ), 41 over-sampling ( ), 46 oversampling method ( ), 46, 50 sigma-delta AD convertor ( AD ), 50 (over-sampling), 46 (oversampling method), 46, 50 (high pass filter, HPF), 41 AD (sigma-delta AD convertor), 50 (band rejection filter, BRF), 41 (band pass filter, BPF), 41 (low pass filter, LPF), 41 (delta modulation), 46 51